Is there a need to diversify my investments across the different roboadvisors in case one closes down?

That is exactly the concern for some investors - especially with what happened with Smartly some time back. So if your assets are held by a custodian in your name, then even if the platform ceases operation, you still own the securities with the custodian, and can possibly continue investing though at a high cost maybe.

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Diversification through different platforms in terms of risk - yes. In terms of the type of capital (cash, srs, cpf) used - yes. But for returns, I think not so much.

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How a typical portfolio would be is that there is a central core portfolio for some steady returns. And alongside, you could have a satellite portfolio in some riskier assets for some boost with minimal extra risk incurred. As robos are structured to be diversified and well-rounded, it wouldn't fit well as a satellite for extra returns. Possible, but not the ideal option.